, Volume 22, Issue 1, pp 399–414 | Cite as

Coherent and convex loss-based risk measures for portfolio vectors



In this paper, we introduce two new classes of risk measures, named coherent and convex loss-based risk measures for portfolio vectors. These new risk measures can be considered as a multivariate extension of univariate loss-based risk measures introduced by Cont et al. (Stat Risk Model 30:133–167, 2013). Representation results for these new introduced risk measures are provided. The links between convex loss-based risk measures for portfolios and convex risk measures for portfolios introduced by Burgert and Rüschendorf (Insur Math Econ 38:289–297, 2006) or Wei and Hu (Stat Probab Lett 90:114–120, 2014) are stated. Finally, applications to the multi-period coherent and convex loss-based risk measures are addressed.


Convex loss-based risk measures Coherent loss-based risk measures Risk measures for portfolio vectors Multi-period risk measures 

Mathematics Subject Classification

91B30 91B32 91B70 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanPeople’s Republic of China

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